The Noise Report is a feature in the game that allows you to see what Drops and stats of enemies that you've faced, as well as see your record of how fast it's taken you to defeat a certain enemy. In the DS version it is unlocked in W1D4.
Achievements and Rewards. Edit
In Solo Remix, you can obtain an achievement for fighting every single Noise in the game.
In the DS version, after getting all the Noise in the Noise Report, you will also be able to see Rhyme in her Noise form with all the characters in the Save Screen. This also happens in Solo Remix, but is now seen on the new Deeds Screen.